Since they don’t respect our sovereignty, neither should we respect theirs. Send the U.S. military in to obliterate the drug cartels, no matter what it takes. Maybe while they’re there, repay Mexico’s insolence with some “reverse remittances” by seizing part of their oil production and using the proceeds to repay the U.S. for all the damage they have done to us. Then seal the border and make it crystal clear that anyone attempting to cross it illegally will be shot on sight. Oh, and implement the tariffs that Trump threatened on Mexican imports and make them permanent.
And this would all be after we’ve rounded up every last illegal in the U.S. and dumped them in Mexico, along with pamphlets directing them to whatever social services Mexico has.
In summary, we should stand on Mexico’s oxygen hose and only let them have a little air when they behave. There are just some parts of the world (sub-Saharan Africa, Latin America, etc.) that are simply incapable of maintaining a civilized society on their own. Those types of people actually benefit from colonization, as those periods in their history are the only ones in which they had some semblance of civilization. Leave them to their own devices, and it all crumbles (see: South Africa). We certainly don’t want to be responsible for running Mexico, but it wouldn’t hurt to make sure they never forget who’s boss.